Within the present application:                “Pulse” will designate a radio-frequency (RF) pulse at the Larmor frequency, which can be either simple (e.g. square) or “composite”, comprising a succession of simple pulses, called sub-pulses or elementary pulses, and, possibly gradient blips. A pulse is designed to induce a predetermined rotation of nuclear spins. It can be characterized by a complex envelope modulating a radio-frequency carrier at the Larmor frequency.        “Pulse train” will designate a succession of pulses, either simple or composite, each inducing a respective rotation of nuclear spins.        “Refocusing pulse/pulse train” will designate a pulse/pulse train designed to refocus nuclear spin in the transverse plane (i.e. in a plane perpendicular to the magnetization, or longitudinal, magnetic field B0).        “Inversion pulse” will designate a pulse, either simple or composite, designed for rotating nuclear spins by 180°, or π radians. An inversion pulse can be used for refocusing.        “Excitation pulse” will designate a pulse, either simple or composite, designed for flipping nuclear spins initially aligned along the direction of B0.        “Pulse sequence” or simply “sequence” will designate a full MRI sequence comprising at least an excitation pulse and possibly inversion and/or refocusing pulse(s).        “B1” will designate the radio-frequency field at the Larmor frequency associated to pulses. B1 can be written as the sum of two counter-rotating circularly-polarized fields: B1+, rotating in the same direction as the nuclear spins, and B1−, rotating in the opposite direction. Only B1+ contributes to rotating and flipping spins.        
The invention applies in particular, albeit not exclusively, to T2-weighted imaging, more particularly when performed at Ultra-High magnetic Field (e.g. 7 Tesla and above), when B0 and B1 non-uniformities become a major concern. The inventive method can be applied to the design and generation of known sequences based on turbo-spin echo and combined with known techniques such as kT-points and/or parallel-transmission MRI.
T2-weighted imaging is a fundamental MRI technique for the diagnosis of brain diseases or injuries involving gray matter and white matter lesions such as strokes, ischemia and multiple sclerosis [1,2]. T2-weighted imaging is commonly achieved thanks to the spin-echo phenomenon, which consists in reversing the dephasing of the transverse magnetization to create a signal echo. RARE imaging [3] (also known as Turbo Spin Echo or Fast Spin Echo) increases the speed of spin-echo imaging by acquiring a series of spin echoes with different phase encodings after each excitation. Later developments on RARE were aimed at reducing and continuously varying the flip angle of the refocusing pulses as a useful means of addressing high radiofrequency (RF) power deposition and typical RARE image artifacts such as blurring [4,5]. The variable flip angle turbo spin echo sequence, referred to as “SPACE” (Sampling Perfection with Application optimized Contrasts using different flip angle Evolution) [6], is now among the most commonly employed 3D sequences to obtain T2-weighted anatomical images of the brain. To this end, an excitation pulse is followed by a long variable angle refocusing pulse train acquiring an entire k-space partition plane per repetition (TR). Careful adjustment of the targeted angles and the echo spacing between the acquisition blocks, as well as the usual imaging parameters, allows excellent contrast between gray matter (GM), white matter (WM) and Cerebrospinal fluid (CSF) at field strengths up to 3 Tesla [5].
T2-weighted imaging should benefit from the increased signal-to-noise ratio available at high field strengths (7 Tesla and beyond) to enable higher spatial resolution acquisitions and hence better visualization of small structures and fluid interfaces of the brain. However, as mentioned above, when moving towards Ultra High Fields (UHF), the increased resonance frequency of proton nuclei (297 MHz at 7 Tesla) causes the RF wavelength to become smaller than the human brain, leading to an inhomogeneous distribution of the transmit magnetic field (B1+). This spatial B1+ inhomogeneity gives rise not only to variations in signal intensity for a given tissue across the brain, but more importantly, to different levels of contrast in the same image [7]. Parallel transmission (pTX) [8,9] has been repeatedly shown to successfully mitigate these issues. This technique utilizes multiple independently-driven coil elements distributed around the subject. In its simplest form, referred to as RF-Shimming [10], the B1+ fields from all coil elements are combined optimizing the amplitude and phase of each array element, while keeping the waveforms identical, to optimize the B1+ distribution in a region of interest (ROI). RF-shimming has already demonstrated its ability to mitigate the B1+ field inhomogeneity at 3 T in the context of T2-weighted imaging with a TSE sequence [11]. Further generalization of this concept led to the introduction of Transmit-SENSE, exploiting the full potential of the transmit-array by tailoring the RF waveforms to apply to each of the individual coil-elements. This transmission generally occurs in concert with magnetic field gradients to provide additional degrees of freedom in order to maximize the final excitation uniformity.
In that framework, whole-brain non-selective uniform spin excitations were demonstrated at 7 Tesla using a kT-point trajectory [12]. This technique proposes a minimalistic transmit k-space trajectory concentrated around the center of k-space to compensate for the smooth RF inhomogeneities present in volumes such as the human brain. This method was then extended to large tip angles. Using optimal control theory [13] and when applied to MP-RAGE T1-weighted imaging, such pulses were shown to provide excellent spatial uniformity throughout the human brain [14]. On the other hand, when dealing with refocusing properties of RF pulses, most work carried out so far has exclusively been in 2D and has relied on a state description of the dynamics and on the, not always fulfilled, linear class of large tip angle (LCLTA) criteria [15] to presume consistent behavior for arbitrary states [16]. The non-selective refocusing pulses included in the 3D spin-echo (SE) and turbo-spin-echo (TSE) sequences, all relevant for T2-weighted imaging at UHF have only seldom been addressed.
Reference [17] discloses a MRI method wherein self-refocused kT-points pulses are placed in a SPACE sequence and provided T2-weighted images of improved quality in terms of signal and contrast homogeneity. However in that study, only one RF pulse was designed and subsequently scaled for the whole RF echo train, an approximation that worsens with the angle value. A purely transverse rotation axis was also assumed by imposing self-refocused pulses [15], likewise an approximation that deteriorates at high flip angle values and when there are off-resonance effects.
Yet in the same time, further optimized non-selective phase-free refocusing kT-points pulses able to mitigate severe B1+ and ΔB0 inhomogeneities have been investigated to achieve a 180° transverse rotation of the spins, regardless of the initial state of the magnetization at 7 Tesla with pTX [28], thanks to an adaptation of the GRadient Ascent Pulse Engineering algorithm (GRAPE) [18], originally developed for NMR-spectroscopy. The method of reference [19], however, is strictly limited to the case of a single pulse inducing a 180° transverse rotation about a free transverse rotation axis which is not sufficient for carrying out several advanced imaging techniques. Generalization to an arbitrary rotation angle and/or to a train of pulses inducing different rotations about a same axis is not straightforward.